On wild ramification in quaternion extensions

Quaternion extensions are often the smallest extensions to exhibit special properties. In the setting of the Hasse-Arf Theorem, for instance, quaternion extensions are used to illustrate the fact that upper ramification numbers need not be integers. These extensions play a similar role in Galois module structure. To better understand these examples, we catalog the ramification filtrations that are possible in totally ramified extensions of dyadic number fields. Interestingly, we find that the catalog depends, for sharp lower bounds, upon the refined ramification filtration, which is associated with the biquatratic subfield. Moreover these examples, as counter-examples to the conclusion of Hasse-Arf, occur only when the refined filtration is, in two different ways, extreme.Comment: 19 pages. This is an extensive revision of the earlier draf

THE CONSTITUTIONAL SIGNIFICANCE OF DELEGATED LEGISLATION IN ENGLAND

The Committee on Ministers\u27 Powers defined delegated legislation as the exercise by a subordinate authority, such as a Minister, of the legislative power delegated to him by Parliament. This definition followed logically from the terms of reference which required the Committee to report what safeguards are desirable or necessary to secure the constitutional principles of the sovereignty of Parliament and the supremacy of the Law. \u27 Behind these two statements lie certain assumptions which coloured the Report of the Committee and influenced its recommendations. One of these assumptions is that Ministers of the Crown are subordinate to Parliament so that any great increase in their powers may threaten Parliamentary sovereignty. A second assumption is that the phrase legislative power of Parliament is self-explanatory and free from ambiguity. These two assumptions are closely connected for they appear to answer implicitly the questions of the relationship of the Executive to Parliament and of the functions which the latter body performs under the Constitution today

Intersection Information based on Common Randomness

The introduction of the partial information decomposition generated a flurry of proposals for defining an intersection information that quantifies how much of "the same information" two or more random variables specify about a target random variable. As of yet, none is wholly satisfactory. A palatable measure of intersection information would provide a principled way to quantify slippery concepts, such as synergy. Here, we introduce an intersection information measure based on the G\'acs-K\"orner common random variable that is the first to satisfy the coveted target monotonicity property. Our measure is imperfect, too, and we suggest directions for improvement.Comment: 19 pages, 5 figure

Spectroscopy on two coupled flux qubits

We have performed spectroscopy measurements on two coupled flux qubits. The qubits are coupled inductively, which results in a $\sigma_1^z\sigma_2^z$ interaction. By applying microwave radiation, we observe resonances due to transitions from the ground state to the first two excited states. From the position of these resonances as a function of the magnetic field applied we observe the coupling of the qubits. The coupling strength agrees well with calculations of the mutual inductance

Generalized Stacking Fault Energy Surfaces and Dislocation Properties of Silicon: A First-Principles Theoretical Study

The generalized stacking fault (GSF) energy surfaces have received considerable attention due to their close relation to the mechanical properties of solids. We present a detailed study of the GSF energy surfaces of silicon within the framework of density functional theory. We have calculated the GSF energy surfaces for the shuffle and glide set of the (111) plane, and that of the (100) plane of silicon, paying particular attention to the effects of the relaxation of atomic coordinates. Based on the calculated GSF energy surfaces and the Peierls-Nabarro model, we obtain estimates for the dislocation profiles, core energies, Peierls energies, and the corresponding stresses for various planar dislocations of silicon.Comment: 9 figures (not included; send requests to [email protected]

EPR studies of manganese centers in SrTiO3: Non-Kramers Mn3+ ions and spin-spin coupled Mn4+ dimers

X- and Q-band electron paramagnetic resonance (EPR) study is reported on the SrTiO3 single crystals doped with 0.5-at.% MnO. EPR spectra originating from the S = 2 ground state of Mn3+ ions are shown to belong to the three distinct types of Jahn-Teller centres. The ordering of the oxygen vacancies due to the reduction treatment of the samples and consequent formation of oxygen vacancy associated Mn3+ centres are explained in terms of the localized charge compensation. The EPR spectra of SrTiO3: Mn crystals show the presence of next nearest neighbor exchange coupled Mn4+ pairs in the directions.Comment: 17 pages, 8 figure

Linear Chains of Styrene and Methyl-Styrene Molecules and their Heterojunctions on Silicon: Theory and Experiment

We report on the synthesis, STM imaging and theoretical studies of the structure, electronic structure and transport properties of linear chains of styrene and methyl-styrene molecules and their heterojunctions on hydrogen-terminated dimerized silicon (001) surfaces. The theory presented here accounts for the essential features of the experimental STM data including the nature of the corrugation observed along the molecular chains and the pronounced changes in the contrast between the styrene and methyl-styrene parts of the molecular chains that are observed as the applied bias is varied. The observed evolution with applied bias of the STM profiles near the ends of the molecular chains is also explained. Calculations are also presented of electron transport along styrene linear chains adsorbed on the silicon surface at energies in the vicinity of the molecular HOMO and LUMO levels. For short styrene chains this lateral transport is found to be due primarily to direct electron transmission from molecule to molecule rather than through the silicon substrate, especially in the molecular LUMO band. Differences between the calculated position-dependences of the STM current around a junction of styrene and methyl-styrene molecular chains under positive and negative tip bias are related to the nature of lateral electron transmission along the molecular chains and to the formation in the LUMO band of an electronic state localized around the heterojunction.Comment: 17 pages plus 11 figures. To appear in Physical Review

A Preliminary Report on Unique Hail and Tornadic Storm Observations in Central Illinois and Eastern Indiana on 3 April 1974

published or submitted for publicationis peer reviewedOpe

WISE J163940.83-684738.6: A Y Dwarf identified by Methane Imaging

We have used methane imaging techniques to identify the near-infrared counterpart of the bright WISE source WISEJ163940.83-684738.6. The large proper motion of this source (around 3.0arcsec/yr) has moved it, since its original WISE identification, very close to a much brighter background star -- it currently lies within 1.5" of the J=14.90+-0.04 star 2MASS16394085-6847446. Observations in good seeing conditions using methane sensitive filters in the near-infrared J-band with the FourStar instrument on the Magellan 6.5m Baade telescope, however, have enabled us to detect a near-infrared counterpart. We have defined a photometric system for use with the FourStar J2 and J3 filters, and this photometry indicates strong methane absorption, which unequivocally identifies it as the source of the WISE flux. Using these imaging observations we were then able to steer this object down the slit of the FIRE spectrograph on a night of 0.6" seeing, and so obtain near-infrared spectroscopy confirming a Y0-Y0.5 spectral type. This is in line with the object's near-infrared-to-WISE J3--W2 colour. Preliminary astrometry using both WISE and FourStar data indicates a distance of 5.0+-0.5pc and a substantial tangential velocity of 73+-8km/s. WISEJ163940.83-684738.6 is the brightest confirmed Y dwarf in the WISE W2 passband and its distance measurement places it amongst the lowest luminosity sources detected to date.Comment: Accepted for publication in The Astrophysical Journal, 20 September 201

A second order minimality condition for the Mumford-Shah functional

A new necessary minimality condition for the Mumford-Shah functional is derived by means of second order variations. It is expressed in terms of a sign condition for a nonlocal quadratic form on $H^1_0(\Gamma)$, $\Gamma$ being a submanifold of the regular part of the discontinuity set of the critical point. Two equivalent formulations are provided: one in terms of the first eigenvalue of a suitable compact operator, the other involving a sort of nonlocal capacity of $\Gamma$. A sufficient condition for minimality is also deduced. Finally, an explicit example is discussed, where a complete characterization of the domains where the second variation is nonnegative can be given.Comment: 30 page